N. Flytzanis

Kink, breather and asymmetric envelope or dark solitons in nonlinear chains. I. Monatomic chain

The authors have examined and obtained analytic expressions for the basic nonlinear excitations in a monoatomic chain with cubic and quartic interatomic potentials and verified their stability under collision. They determined bounds on the potential parameters for which kink, breather, envelope and dark solitons exist. The kink and the envelope of a soliton are determined in the long-wavelength approximation, while the oscillations of the carrier in the envelope soliton are treated exactly. The introduction of second-neighbour interactions (SNI) changes drastically the character of the solutions. Kinks are supersonic if the dispersive term is positive and subsonic if it is negative. In a cubic potential the envelope solitons are asymmetric (there is a net displacement). There is a switch from a kink to a symmetric envelope as the potential parameters are changed; these parameters also determine the regions for which plane waves are unstable. The above excitations can be created by using arbitrary initial conditions which, however, have a net displacement for kinks and the correct Fourier components for an envelope soliton. The asymmetric envelope solitons explain earlier computer simulations using as initial conditions optical gaussian pulses.

Josephson effect in double-barrier superconductor-ferromagnet junctions

We study the Josephson effect in ballistic double-barrier SIFIS planar junctions, consisting of bulk superconductors (S), a clean metallic ferromagnet (F), and insulating interfaces (I). We solve the scattering problem based on the Bogoliubov-de Gennes equations and derive a general expression for the dc Josephson current, valid for arbitrary interfacial transparency and Fermi wave vectors mismatch (FWVM). We consider the coherent regime in which quasiparticle transmission resonances contribute significantly to the Andreev process. The Josephson current is calculated for various parameters of the junction, and the influence of both interfacial transparency and FWVM is analyzed. For thin layers of strong ferromagnet and finite interfacial transparency, we find that coherent (geometrical) oscillations of the maximum Josephson current are superimposed on the oscillations related to the crossovers between 0 and π states. For the same case we find that the temperature-induced 0- π transition occurs if the junction is very close to the crossover at zero temperature.

Discrete lattice solitons: properties and stability

The authors present a detailed numerical study of the dynamics of high-energy kink excitations in monatomic chains, with a simple description using a microscopic model of the narrow kink core. They present velocity-amplitude and energy-momentum curves for the kink which fit well the numerical results. Kink-kink collisions are slightly inelastic depending on the velocities and point of collision within a lattice spacing.

Wave Modulations in the Nonlinear Biinductance Transmission Line

Adding dissipative elements to a discrete biinductance transmission line which admits both low frequency (LF) and high frequency (HF) modes, dynamics of a weakly nonlinear modulated wave is investigated theoretically and numerically. In the semidiscrete approximation using a proposed decoupling ansatz for the voltage of the two different cells, it is shown that the original differential-difference equation for this transmission line can be reduced to the complex Ginzburg–Landau (CGL) equation. The modulational instability criterion for sinusoidal waves has been recovered. Furthermore, numerical simulations show that the theoretical predictions are well reproduced.

A Semi-Linear Elliptic Pde Model For The Static Solution Of Josephson Junctions

In this study we derive a semi-linear Elliptic Partial Differential Equation (PDE) problem that models the static (zero voltage) behavior of a Josephson window junction. Iterative methods for solving this problem are proposed and their computer implementation is discussed. The preliminary computational results that are given, show the modeling power of our approach and exhibit its computational efficiency.

Solition resonances in atomic nonlinear systems

Abstract For competitive first and second neighbor interactions in a monatomic chain there are subsonic solitons which are unstable at low velocities and resonantly split in two stable solitons with high velocities. The process is consistent with the conservation laws, which are exactly satisfied by the splitting process. There are also divergent instabilities. The effect of the second neighbor nonlinear interactions on the threshold velocities for resonant or divergent instabilities is studied. The collision of two solitons near resonance shows large phase shifts but due to the existence of a linear instability mode the solitons separate eventually. The effect of the form of the interatomic law is also discussed.

Stability analysis of static solutions in a Josephson junction

We present all the possible solutions of a Josephson junction with bias current and magnetic field with both inline and overlap geometry, and examine their stability. We follow the bifurcation of new solutions as we increase the junction length. The analytical results are in terms of elliptic functions for the case of inline geometry, and are in agreement with the numerical calculations, explaining also the strong hysteretic phenomena typically seen in the calculation of the maximum tunnelling current. This suggests a different experimental approach based on the use, instead of the external magnetic field, of the modulus of the elliptic function or the related quantity the total magnetic flux to avoid hysteretic behaviour and unfold the overlapping Imax (H ) curves.

Effect Of Geometry On Fluxon Width In A Josephson Junction

We investigate the electromagnetic influence of the surrounding idle (no tunneling) region on static fluxons in window Josephson junctions. We calculated the fluxon width as a function of the size of the idle region for three different window (active tunneling area) geometries, namely elongated truncated rhombus, rectangular and bow-tie and derived approximate expressions for the case of small and large idle regions. The window geometry affects both the fluxon width and the fluxon stability. One can define an effective λJ which depends on the junction width, the idle region width and the inductance ratio and has important consequences on the static and dynamic properties of window Josephson junctions. We also show the effect of the idle region on the maximum tunneling current as a function of the external magnetic field.

The window Josephson junction: a coupled linear nonlinear system

Abstract We investigate the interface coupling between the two-dimensional sine-Gordon equation and the two-dimensional wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the domain as well as the electrical coupling parameters are considered. When the linear region is located at each end of the nonlinear domain, we derive an effective one-dimensional model, and using soliton perturbation theory, compute the fixed points that can trap either a kink or antikink at an interface between two sine-Gordon media. This approximate analysis is validated by comparing with the solution of the partial differential equation and describes kink motion in the one-dimensional window junction. Using this, we analyze steady-state kink motion and derive values for the average speed in the one- and two-dimensional systems. Finally, we show how geometry and the coupling parameters can destabilize kink motion.

Split Mode Method for the Elliptic 2D Sine-Gordon Equation: Application to Josephson Junction in Overlap Geometry

We introduce a new type of splitting method for semilinear partial differential equations. The method is analyzed in detail for the case of the two-dimensional static sine-Gordon equation describing a large area Josephson junction with overlap current feed and external magnetic field. The solution is separated into an explicit term that satisfies the one-dimensional sine-Gordon equation in the y-direction with boundary conditions determined by the bias current and a residual which is expanded using modes in the y-direction, the coefficients of which satisfy ordinary differential equations in x with boundary conditions given by the magnetic field. We show by direct comparison with a two-dimensional solution that this method converges and that it is an efficient way of solving the problem. The convergence of the y expansion for the residual is compared for Fourier cosine modes and the normal modes associated to the static one-dimensional sine-Gordon equation and we find a faster convergence for the latter. Even for such large widths as w=10 two such modes are enough to give accurate results.